A mixture containing primarily liquid and fine particles therein, such as waste water, can be initially treated by flowing the mixture into a tank along with myriad microscopic air bubbles that float a large portion of the particles at the surface of the liquid. The fine particles are skimmed from the surface and tend to stick together to form sludge, with the sludge dropped into a conveyor that moves it. Our earlier U.S. Pat. No. 5,091,083 shows a system of this type. Once the sludge has been moved out of the boundaries of the tank by the conveyor, it is usually pumped to a dewatering facility that compresses the sludge to remove almost all liquid therein. This allows the sludge to be efficiently disposed of, as by drying in the sun and used to form construction material or otherwise disposed of. Efficient pumps for pumping the sludge from the conveyor to the final dewater apparatus include rotating vanes that cut the sludge while pumping it. Before the pumped sludge is finally dewatered, a polymer is added to the sludge to recoalesce it. Although only one to one hundred parts per million of polymer is added to the sludge, the polymer is expensive (e.g. $3.00 per pound). A system for dewatering sludge which was of low cost, occupied minimal space, and avoided the need to pump the sludge, would be of value.